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Research Article | Open Access

A volume constraint problem for the nonlocal doubly nonlinear parabolic equation

Masashi Misawa1, Kenta Nakamura2( ), Yoshihiko Yamaura3
Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan
Headquarters for Admissions and Education, Kumamoto University, Kumamoto 860-8555, Japan
Department of Mathematics, College of Humanities and Sciences, Nihon University, Tokyo 156-8550, Japan
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Abstract

We consider a volume constraint problem for the nonlocal doubly nonlinear parabolic equation, called the nonlocal p-Sobolev flow, and introduce a nonlinear intrinsic scaling, converting a prototype nonlocal doubly nonlinear parabolic equation into the nonlocal p-Sobolev flow. This paper is dedicated to Giuseppe Mingione on the occasion of his 50th birthday, who is a maestro in the regularity theory of PDEs.

Keywords

nonlocal p-Sobolev flownonlinear intrinsic scalingdoubly nonlinear equations

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Mathematics in Engineering
Volume 5 Issue 6,
December 2023
Pages 1-26
DOI: 10.3934/mine.2023098

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Cite this article:
Misawa M, Nakamura K, Yamaura Y. A volume constraint problem for the nonlocal doubly nonlinear parabolic equation. Mathematics in Engineering, 2023, 5(6): 1-26. https://doi.org/10.3934/mine.2023098

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Received: 29 January 2023
Revised: 13 September 2023
Accepted: 14 September 2023
Published: 15 December 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)